\section{Othello}\label{sec:othello}
Othello is a two-player game played on a board of 8 by 8 squares. Figure
\ref{fig:startpos} shows a screenshot of our application with the starting
position of the game. The white and the black player place at alternate turns
one disc at a time. A move is only valid if the newly placed disc causes one or
more of the opponent's discs to become enclosed. The enclosed discs are then
flipped, meaning that they change color.  If and only if a player cannot capture
any of the opponent's discs the player passes. When both players have to pass
the game is ended. The player who has the most discs of his own colour is
declared winner, when the number of discs of each colour are equal a draw is
declared.

\begin{figure}
  \centering
  \includegraphics[width=0.4\textwidth]{img/application_startpos}
  \caption{Screenshot of the used application showing the starting position of
    the game. The black circles indicate one of the possible moves for the current
    player (black).}
  \label{fig:startpos}
\end{figure}

The best known Othello playing progam is LOGISTELLO \cite{wiering2012neural}.
In 1997, it defeated the then world champion T. Murakami with a score of 6-0.
The program was trained in several steps: First, logistic regression was
used to map the features of the disc differential at the end of the game. Then,
it used 13 different game stages and sparse linear regression to assign values to
pattern configurations. Its evaluation function was then trained on several
millions of training positions to fit approximately 1.2 million weights
\cite{buro1995statistical}.
